1. **Problem statement:** A special 10-faced die numbered 1 to 10 is rolled. We want to find the probability of landing on: (a) an even number (b) a prime number (c) the number 11 (d) a square number 2. **Formula for probability:** $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 3. **Step (a) Even numbers:** The even numbers on the die are 2, 4, 6, 8, 10. Number of favorable outcomes = 5 Total outcomes = 10 $$P(\text{even}) = \frac{5}{10} = \frac{1}{2}$$ 4. **Step (b) Prime numbers:** Prime numbers between 1 and 10 are 2, 3, 5, 7. Number of favorable outcomes = 4 $$P(\text{prime}) = \frac{4}{10} = \frac{2}{5}$$ 5. **Step (c) Number 11:** 11 is not on the die, so favorable outcomes = 0 $$P(11) = \frac{0}{10} = 0$$ 6. **Step (d) Square numbers:** Square numbers between 1 and 10 are 1 and 4. Number of favorable outcomes = 2 $$P(\text{square}) = \frac{2}{10} = \frac{1}{5}$$ **Final answers:** (a) $\frac{1}{2}$ (b) $\frac{2}{5}$ (c) $0$ (d) $\frac{1}{5}$